In this paper it is shown that
the problem of solving the triple series equations of the first kind
∑n=0∞AnΓ(α + 1 + n)Ln(α;x)
= 0, 0 ≦ x < a,
(1)
∑n=0∞AnΓ(α + β + n)Ln(α;x)
= f(x), a < x < b,
(2)
∑n=0∞AnΓ(α + 1 + n)Ln(α;x)
= 0, b < x < ∞,
(3)
and the triple series equations of the second kind
∑n=0∞BnΓ(α + β + n)Ln(α;x)
= g(x), 0 ≦ x < a,
(4)
∑n=0∞BnΓ(α + 1 + n)Ln(α;x)
= 0, a < x < b,
(5)
∑n=0∞BnΓ(α + β + n)Ln(α;x)
= h(x), b < x < ∞,
(6)
where α + β > 0,0 < β < 1, Ln(α;x) = Lnα(x) is the Laguerre polynomial and
f(x), g(x) and h(x) are known functions, can be reduced to that of solving a
Fredholm integral equation of the second kind. The analysis is formal and no attempt
is made to supply details of rigour.
